Nanorobots for Targeted Drug Delivery in Biofilm Removal / Exotic patterns in Quasi-Ring Networks

Veit-Holt: Biofilms are structured communities of microorganisms embedded in an extracellular polymeric substance, or EPS, matrix. That matrix protects cells from antibiotics, mechanical removal, and other environmental stresses, which is why biofilms are especially difficult to eliminate in dental, medical, and industrial settings. This presentation examines how magnetic nanorobots may address that problem through targeted transport, mechanical disruption, and localized chemical action. In addition to the biological motivation, the talk introduces several simple mathematical ideas that clarify why these systems behave the way they do: continuum transport models for biofilm growth, reaction-diffusion limits on drug penetration, low-Reynolds-number propulsion, magnetic force balance, and a viscoelastic description of EPS resistance. Together, these ideas show why passive treatment often fails and why actively controlled nanoscale devices are promising for targeted biofilm removal.

Debnath: Pattern formation in network-coupled dynamical systems arises in many physical, chemical, and biological contexts. In this work, we study reaction–diffusion dynamics on networks, with a focus on quasi-ring topologies. The dynamics are modeled using a two-species system, where diffusion is represented through the graph Laplacian. The stability of the homogeneous steady state is analyzed using the Master Stability Function (MSF) framework by decomposing perturbations into Laplacian eigenmodes. To capture the nonlinear evolution near instability, weakly nonlinear theory is employed, yielding amplitude equations that describe pattern growth and saturation. Numerical simulations of the Brusselator model are performed on both regular ring and perturbed quasi-ring networks. While the regular ring supports spatially extended patterns associated with delocalized Fourier modes, small perturbations in the quasi-ring break symmetry and induce localization of Laplacian eigenvectors. In particular, localized eigenvectors associated with short-wave instabilities interact with delocalized modes from long-wave instabilities, significantly shaping the resulting patterns. As a result, quasi-ring networks exhibit a range of dynamical behaviors, including synchronized oscillations, oscillation death, traveling waves, and mixed states with coexisting stationary and oscillatory regions. These findings highlight how small structural perturbations can strongly influence network spectra and lead to complex, chimera-like pattern formation.